1) Derive the expression for the transition rate from to for the matrix element that varies harmonically in time as . 2)Starting from the definition of the potential due to acoustic phonons, derive the expression for the electron scattering rate with acoustic phonons that was given in class. 3)The expression for optical scattering derived in class was for parabolic bands, extend the formulation to include the effects of ellipsoidal, nonparabolic bands, like the ones you find in silicon.